Question: Solve for $x$ and $y$ using elimination. ${-2x-6y = -66}$ ${2x+5y = 58}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $-y = -8$ $\dfrac{-y}{{-1}} = \dfrac{-8}{{-1}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {-2x-6y = -66}\thinspace$ to find $x$ ${-2x - 6}{(8)}{= -66}$ $-2x-48 = -66$ $-2x-48{+48} = -66{+48}$ $-2x = -18$ $\dfrac{-2x}{{-2}} = \dfrac{-18}{{-2}}$ ${x = 9}$ You can also plug ${y = 8}$ into $\thinspace {2x+5y = 58}\thinspace$ and get the same answer for $x$ : ${2x + 5}{(8)}{= 58}$ ${x = 9}$